The crucial properties of such a light axion are generic and do not depend on the details of the putative UV completion. An important byproduct of this construction is an enhancement of all axion interactions which is universal, that is, model-independent and equal for all axion couplings, at fixed \(m_a\) . The detailed exploration of the \(Z_{\cal N}\)  paradigm and of the phenomenological constraints which do not require the axion to account for DM can be found in Ref. [1]}.
